{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T09:18:12Z","timestamp":1762420692558,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comment. Math. Helv."],"published-print":{"date-parts":[[2017,7,27]]},"abstract":"<jats:p>\n                    We provide a direct construction of a cycle map in the level of representing complexes from the motivic cohomology of real (or complex) varieties to the appropriate ordinary cohomology theory. For complex varieties, this is simply integral Betti cohomology, whereas for real varieties the recipient theory is the bigraded\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{Gal}(\\mathbb C\/\\mathbb R)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -equivariant cohomology [19]. Using the finite analytic correspondences from [7] we provide a sheaf-theoretic approach to ordinary equivariant\n                    <jats:inline-formula>\n                      <jats:tex-math>RO(G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -graded cohomology for any finite group\n                    <jats:inline-formula>\n                      <jats:tex-math>G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In particular, this gives a complex of sheaves\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb Zp_{\\omega}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    on a suitable equivariant site of real analytic manifolds-with-corner whose construction closely parallels that of the Voevodsky's motivic complexes $$\\mathbb Zp_{\\mathcal M}\n                    <jats:inline-formula>\n                      <jats:tex-math>. Our cycle map is induced by the change of sites functor that assigns to a real variety<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    X\n                    <jats:inline-formula>\n                      <jats:tex-math>its analytic space<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    X(\\mathbb C)$ together with the complex conjugation involution.\n                  <\/jats:p>","DOI":"10.4171\/cmh\/416","type":"journal-article","created":{"date-parts":[[2017,7,27]],"date-time":"2017-07-27T17:45:01Z","timestamp":1501177501000},"page":"429-465","source":"Crossref","is-referenced-by-count":0,"title":["An explicit cycle map for the motivic cohomology of real varieties"],"prefix":"10.4171","volume":"92","author":[{"given":"Pedro F.","family":"dos Santos","sequence":"first","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Lisbon, Portugal"}]},{"given":"Robert M.","family":"Hardt","sequence":"additional","affiliation":[{"name":"Rice University, Houston, USA"}]},{"given":"James D.","family":"Lewis","sequence":"additional","affiliation":[{"name":"University of Alberta, Edmonton, Canada"}]},{"given":"Paulo","family":"Lima-Filho","sequence":"additional","affiliation":[{"name":"Texas A&M University, College Station, USA"}]}],"member":"2673","container-title":["Commentarii Mathematici Helvetici"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/CMH\/416","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T09:12:54Z","timestamp":1762420374000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/cmh\/416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,27]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/cmh\/416","relation":{},"ISSN":["0010-2571","1420-8946"],"issn-type":[{"type":"print","value":"0010-2571"},{"type":"electronic","value":"1420-8946"}],"subject":[],"published":{"date-parts":[[2017,7,27]]}}}